Results 1 to 10 of about 82,785 (291)
SoftwareXThe conformal mapping function from the interior of the complex plane's unit circle to the exterior of any simple closed curve on the real plane finds widespread applications, including the use of complex variable methods in elasticity studies.
Kai He, Kai Wang
doaj +4 more sources
Simple closed curves contained in ε-boundaries of planar sets
Applied General TopologyThe ε-boundary of a set A ⊆ R2 is the set { p ∈ R2 : ρ(p,A) = ε } , where ρ is the Euclidean distance. We prove that if A,B ⊆ R2 are nonempty, connected sets, A is bounded, and 0< ε < ρ(A,B), then the ε-boundary of A contains a simple closed curve (aka a
Mikhail Patrakeev, Aleksei Volkov
doaj +3 more sources
The span and semispan of some simple closed curves [PDF]
Proceedings of the American Mathematical Society, 1991 The spans of simple closed curves that are boundaries of convex regions are determined. The following question of Lelek is answered affirmatively for these curves: Are the span and the semispan of a simple closed curve equal? The same answer is obtained in the case of nonconvex quadrilaterals.
Katarzyna Tkaczyńska
openalex +2 more sources
Self-unlinked simple closed curves [PDF]
Transactions of the American Mathematical Society, 1965 interiors of a collection of disjoint 3-cells each of diameter less than S. A set X is locally tame at p if p has a closed neighborhood in X which is a tame complex in M. If X is not locally tame at p then p is a wild point of X. A set is called nicely wild if the union of its wild points is a tame 0-dimensional set.
David W. Henderson
openalex +3 more sources
Concerning Approachability of Simple Closed and Open Curves [PDF]
Transactions of the American Mathematical Society, 1920 Schoenfliest was the first to formulate the converse of the fundamental theorem of C. Jordant that a simple closed curve? lying wholly within a plane decomposes the plane into an inside and an outside region. The statement of this converse theorem is as follows: Suppose K is a closed, bounded set of points lying in a plane S and that S K = Sl +-S2 ...
J. R. Kline
openalex +2 more sources
Topologically faithful fitting of simple closed curves [PDF]
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004 Implicit representations of curves have certain advantages over explicit representation, one of them being the ability to determine with ease whether a point is inside or outside the curve (inside-outside functions). However, save for some special cases, it is not known how to construct implicit representations which are guaranteed to preserve the ...
D Keren
exaly +4 more sources
A remarkable simple closed curve: revisited [PDF]
Proceedings of the American Mathematical Society, 1981 It is shown that the pathology of R. H. Fox’s remarkable simple closed curve is in a sense explained below more complicated than that of some examples of the well-known Fox-Artin paper.
O. G. Harrold
openalex +2 more sources
Veech surfaces and simple closed curves [PDF]
Israel Journal of Mathematics, 2016 12 pages. v2: added proof of continuity of infimal length functions on quadratic differential space; 16 pages, one figure; to appear in Israel J ...
Max Forester, Robert L. Tang, Jing Tao
openalex +5 more sources
On hyperspaces of knots and planar simple closed curves [PDF]
Topology and its ApplicationsWe consider the Vietoris hyperspaces $\mathcal S(\mathbb R^n)$ of simple closed curves in $\mathbb R^n$, $n=2,3$, and their subspaces $\mathcal S_P(\mathbb R^2)$ of planar simple closed polygons, $\mathcal K_P$ of polygonal knots, and $\mathcal K_T$ of tame knots.
Paweł Krupski, Krzysztof Omiljanowski
openalex +3 more sources
AN ALGEBRAIC CHARACTERIZATION OF SIMPLE CLOSED CURVES ON SURFACES WITH BOUNDARY [PDF]
Journal of Topology and Analysis, 2010 We prove that a conjugacy class in the fundamental group of a surface with boundary is represented by a power of a simple curve if and only if the Goldman bracket of two different powers of this class, one of them larger than two, is zero. The main theorem actually counts self-intersection number of a primitive class by counting the number of terms ...
Moira Chas, Fabiana Krongold
openalex +5 more sources